Question: A wooden block is 4 inches long, 4 inches wide, and 1 inch high. The block is painted red on all six sides and then cut into sixteen 1 inch cubes. How many of the cubes each have a total number of red faces that is an even number?

[asy]

size(4cm,4cm);

pair A,B,C,D,E,F,G,a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r;

A=(0.5,0.1);
B=(0.5,0);
C=(0,0.5);
D=(1,0.5);
E=C+(D-A);
F=C+(B-A);
G=D+(B-A);

draw(A--D--E--C--A--B--G--D);
draw(C--F--B);

a=(3/4)*F+(1/4)*B;
b=(1/2)*F+(1/2)*B;
c=(1/4)*F+(3/4)*B;

m=(3/4)*C+(1/4)*A;
n=(1/2)*C+(1/2)*A;
o=(1/4)*C+(3/4)*A;

j=(3/4)*E+(1/4)*D;
k=(1/2)*E+(1/2)*D;
l=(1/4)*E+(3/4)*D;

draw(a--m--j);
draw(b--n--k);
draw(c--o--l);

f=(3/4)*G+(1/4)*B;
e=(1/2)*G+(1/2)*B;
d=(1/4)*G+(3/4)*B;

r=(3/4)*D+(1/4)*A;
q=(1/2)*D+(1/2)*A;
p=(1/4)*D+(3/4)*A;

i=(3/4)*E+(1/4)*C;
h=(1/2)*E+(1/2)*C;
g=(1/4)*E+(3/4)*C;

draw(d--p--g);
draw(e--q--h);
draw(f--r--i);

[/asy]
Explanation: Each of the 4 corner cubes has 4 red faces. Each of the 8 other cubes on the edges has 3 red faces. Each of the 4 central cubes has 2 red faces. Then, each of the corner cubes and each of the central cubes has an even number of red faces. There are $\boxed{8}$ such cubes.

[asy]

size(4cm,4cm);

pair A,B,C,D,E,F,G,a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r;

A=(0.5,0.1);
B=(0.5,0);
C=(0,0.5);
D=(1,0.5);
E=C+(D-A);
F=C+(B-A);
G=D+(B-A);

draw(A--D--E--C--A--B--G--D);
draw(C--F--B);

a=(3/4)*F+(1/4)*B;
b=(1/2)*F+(1/2)*B;
c=(1/4)*F+(3/4)*B;

m=(3/4)*C+(1/4)*A;
n=(1/2)*C+(1/2)*A;
o=(1/4)*C+(3/4)*A;

j=(3/4)*E+(1/4)*D;
k=(1/2)*E+(1/2)*D;
l=(1/4)*E+(3/4)*D;

draw(a--m--j);
draw(b--n--k);
draw(c--o--l);

f=(3/4)*G+(1/4)*B;
e=(1/2)*G+(1/2)*B;
d=(1/4)*G+(3/4)*B;

r=(3/4)*D+(1/4)*A;
q=(1/2)*D+(1/2)*A;
p=(1/4)*D+(3/4)*A;

i=(3/4)*E+(1/4)*C;
h=(1/2)*E+(1/2)*C;
g=(1/4)*E+(3/4)*C;

draw(d--p--g);
draw(e--q--h);
draw(f--r--i);

[/asy]